Question

Consider the following annual coupon bond with a face value of $1,000, a price of $922.69, a coupon rate of 5.9% and a maturity of 30 years. Right after you purchase the bond, market interest rates change to 12% and remain constant. What would be your realized yield to maturity if you sold the bond after 8 years?

Answer 1

Bond purchase on $922.69 and sold after 8 years.

First calculate selling price

FV = $1000, N = 30 – 8 = 22 years, PMT = 1000*0.059 = $59, YTM = 12%

PV = (PMT/r)*[1 – 1/(1+r)^N] + FV/(1+r)^N

PV = (59/0.12)*(1 – 1/1.12^22) + 1000/1.12^22 = 533.68

Now calculate yield for holder bond for 8 years

PV = $922.69, N = 8, PMT = $59, FV = $533.68; compute r =?

r = 1.37%; this is the actual or realized yield for holder bond for 8 years.